Bell-certified retardance polarimetry from CHSH correlators

Bell--CHSH measurements with polarization-entangled photons are usually reported only as nonlocality witnesses. Here we show that, for retardance sensing, the same coincidence data can also provide a quantitative metrological certificate. For a local birefringent phase $\phi$ encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators $E_{xy}(\phi)$ and obtain an explicit lower bound in terms of the measured correlators and the phase slope $S'(\phi)$ of the Bell parameter. In the unbiased-marginal two-qubit regime, this leads to a dual-use result: the canonical CHSH analyzer settings are simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation. We further show that the certificate remains informative under visibility loss, finite counts, and moderate departure from the Bell-violation threshold, so useful retardance sensitivity can persist even when nonlocality certification is weak or absent. Relative to tomography-based entangled-photon polarimetry, the method converts a standard Bell-calibration run into a sensitivity statement with rigorous lower confidence bounds using only coincidence correlators. The scheme is implementable with standard SPDC sources, wave plates, and polarizing beam splitters.